To install a new garage door spring, you will first need to know the type of spring it uses. Extension spring and torsion spring are the two types of garage door springs. Once you figure that out you can install the new one.
Step 1 - Lift Door
Lift the door to a fully open position. Place a pair of locking pliers under the bottom-most roller which runs in the door track.
Step 2 - Remove Broken Spring
Remove the leftover of the broken spring. Check the pulleys and replace them if there is a major damage.
Step 3 - Replace It
Buy two new springs identical in length and diameter as the broken spring. Replace the broken spring. Don't remove the unbroken spring while replacing the broken one. Ensure that the spring is stretched about 1 inch when the door is fully open.
Step 4 - Remove Unbroken Spring
Move the locking pliers to the other side and remove the unbroken spring in the same way. Remove the locking pliers and lower the door fully. If the door is still heavy to lift, open the door, place the locking pliers and stretch the spring out by 1 to 2 inches. Don't exceed the gap between the two pulleys when the door is fully closed.
Step 5 - Add a Safety Cable
Add a safety cable during this garage door spring installation if it's not there. It prevents the spring when it breaks from shooting at something or somebody.